Elliptic algebras are associative $\Z_{\ge0}$-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying Poincare-Birkhoff- Witt condition. These algebras depend on two continuous parameters, namely, on an elliptic curve and a point on this curve. They are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras will be described, together with their relations to integrable systems, deformation quantization, moduli spaces and other directions of modern investigations.